1. Field of the Invention
Embodiments of the present invention relate to control systems, and particularly, to adaptive control architectures for uncertain dynamic systems.
2. Background of Related Art
An adaptive controller is a controller that makes adjustments, i.e., adaptations, to control an uncertain system. Uncertain systems are systems that can have fixed or time varying parameters with values that are only approximately known. Examples of these parameters include, but are not limited to, aerodynamic coefficients of aircraft, mode shapes of vibrating structures, and parameters associated with dynamics of turbine engines, combustion processes, and chemical reactions. The variations in the parameters may be due to changes in the operation of a system or process, or may be due to other factors, such as, for example, releasing a payload, docking in space, or unknown failures in subsystem components.
Existing adaptive controllers are used to control several types of systems, or “plants,” as they are known in the art. They are frequently used, for example and not limitation, to control automobile and aircraft engines and in aircraft flight controls.
Many types of adaptive controllers are known. Some adaptive controllers, for example, attempt to control uncertain systems by employing a state observer. The state observer provides an estimate of the system's internal state using measurements, or sensed quantities, of the uncertain system. The adaptive controller can then adapt to these sensed quantities and provide an output that stabilizes the uncertain system.
Generally, research in adaptive control is motivated by the desire to maintain a specified level of performance in the presence of modeling errors. Performance is usually measured by the reaction speed of a response to an externally generated command, and the ability of the response to accurately track the externally generated command as measured by the difference between the response and the corresponding commanded value. Modeling errors are usually caused by uncertainties associated with dynamic responses of the systems being controlled.
Adaptive controllers can be classified as either state feedback or output feedback. State feedback controllers, for example, can have computationally simpler adaptive control algorithms compared to output feedback algorithms. This can be because, for example, state feedback controllers do not require the use of a state observer. Output feedback adaptive controllers, however, are required for applications in which it is impractical or impossible to sense the entire state of the process or system under control. Examples of such processes or systems include, but are not limited to, active noise suppression, active control of flexible space structures, fluid flow control systems, combustion control processes, control of chemical processes, automotive control systems, flight control of large flexible aircraft and launch vehicles, and low cost or expendable unmanned aerial vehicles. Models for these applications vary from reasonably accurate low frequency models, e.g., in the case of structural control problems, to less accurate low order models, e.g., in the case of active control of noise, vibrations, flows, and combustion processes.
There have been a number of proposed approaches for the design of output feedback adaptive controllers. All of these approaches contain inherent limitations. Some approaches rely on high gain observers, for example, to reconstruct the states of the controlled process that are not available for feedback. High gain approaches, however, are often impractical due to, for example, the amplification of sensor noise and the potential for unstable responses due to unmodeled high frequency dynamics. Other approaches use an output feedback adaptive controller with an error observer instead of a state observer. These approaches are undesirable, however, because they require unnecessarily complex designs and rely on high gains, which can lead to unstable responses.
Incorporating an adaptive controller for uncertain dynamic systems can mean the replacement of an existing control system. It is highly desirable, however, for an adaptive approach to simply augment an existing controller. Recently, one approach has introduced an adaptive output feedback design that relies on the properties of so-called LQG/LTR controllers that asymptotically satisfy a strictly positive real condition. See E. Lavretsky, “Adaptive Output Feedback Design Using Asymptotic Properties of LQG/LTR controllers,” AIAA Guidance, Navigation, and Control Conference, Toronto, Canada (2010).
This approach minimizes the complexity of the control architecture, but cannot be used to augment an existing controller design and cannot be applied to systems containing non-minimum phase dynamics. This is because, for example, the stability analysis associated with this approach relies on the fact that the designer can set gains at arbitrary high values. Moreover, like other approaches to output feedback adaptive control, it assumes constant unknown ideal weights. This assumption can cause a less-accurate response when uncertain parameters undergo rapid time variations, during sudden changes in system dynamics, and/or when the system is subjected to a time varying external disturbance. It is therefore undesirable in many scenarios.
Another deficiency of existing approaches to adaptive control is that their weight adaptation laws often employ numerical integration. While the integration can reduce steady state tracking errors, it can also cause a conflict that itself leads to a slowly varying tracking error. The slowly varying tracking error can arise when adaptive controllers that employ integration are used to augment a non-adaptive controller that also employs integration. Thus, to avoid this behavior, it is desirable to use an adaptive controller with a weight update law that does not employ numerical integration.
It would therefore be desirable to have an adaptive controller that does not assume constant unknown ideal weights and instead considers varying ideal weights. Such a controller would be desirable, for example and not limitation, in situations where uncertainties and disturbances undergo variations on the same time scale as that of the system being controlled. The controller should be able to augment an existing non-adaptive control design without modifying the gains of that design, and should be less complex than existing adaptive controllers. The controller should additionally be able to control both minimum phase and non-minimum phase systems and should not require the use of high gains. The controller should also afford freedom in the selection of basis functions used to parameterize the uncertainty within the plant dynamics. The controller should also avoid weight update laws that require numerical integration. It is to such a controller that embodiments of the present invention are primarily directed.